par2qua2 {lmomco} | R Documentation

## Equivalent Quantile Function of Two Distributions

### Description

This function combines two distributions into one by weighting of the two quantile functions by the nonexceedance probability. The distributions are specified by the parameter arguments. The left-tail parameter object is the distribution governing the left tail; the right-tail parameter object is the distribution governing the right tail. The quantile function algebra is

Q(F) = (1-F) times Q_{lefttail}(F) + F times Q_{righttail}(F)

where Q(F) is the equivalent quantile for nonexceedance probability F computed by the tail weigthing. Q_{lefttail}(F) is the left-tail quantile function; Q_{righttail} is the right-tail quantile function. Parameter objects are discussed in `vec2par` and `lmom2par` functions. If the optional `weight` argument is provided, then the multiplication of `1-F` or `F` is replaced by `1-weight` or `weight`, respectively. If `weight=0`, then the quantiles for the right tail are returned, and if `weight=1`, then the quantiles for the left tail are returned.

A word of caution. The resulting weighted quantile function is not checked for monotonic increase with F. This is a required property of quantile functions.

### Usage

    par2qua2(f,leftpara,rightpara,weight=NULL,...)

### Arguments

`f` | Nonexceedance probability (0 <= F <= 1).
`leftpara` | The left-tail parameters from `lmom2par` or similar.
`rightpara` | The right-tail parameters from `lmom2par` or similar.
`weight` | An optional weighting argument to use in lieu of `F`.
`...` | The additional arguments are passed to the quantile function such as `paracheck = FALSE` for the generalized Lambda distribution (`quagld`).

### Value

Quantile value for F from the two distributions.

### Author(s)

W.H. Asquith

### See Also

`par2qua`, `lmom2par`, and `par2cdf2`

### Examples

    # Contrived example
    lmr       <- lmom.ub(rnorm(20))
    leftpara  <- parnor(lmr)
    rightpara <- pargev(lmr)
    combined.median <- par2qua2(0.5,leftpara,rightpara)

    # Bigger example--using Kappa fit to whole sample
    # for the right tail and Normal fit to whole sample
    # for the left tail
    D   <- c(123,523,345,356,2134,345,2365,235,12,235,61)
    LM  <- lmom.ub(D)
    KAP <- parkap(LM)
    NOR <- parnor(LM)
    PP  <- pp(D)
    plot(PP,sort(D),ylim=c(-500,2300))
    lines(PP,par2qua(PP,KAP),col=2)
    lines(PP,par2qua(PP,NOR),col=3)
    lines(PP,par2qua2(PP,NOR,KAP))

[Package lmomco version 0.92 Index]